Bach featured prominently in Spivakovsky's recitals throughout his career. After the Great War he performed a monumental series of historical concertos with the Berlin Philharmonic Orchestra under Maestro Wilhelm Furtwängler, tracing the development of the concerto through the stylistic periods by all major composers from Bach to Brahms. This fifteen-concerto tour de force continued the tradition established by his musical forefather Anton Rubinstein, who was renowned for his gargantuan historical solo recitals. The series was a stellar success and Spivakovsky was hailed as a master of all musical styles, an exceptional exponent of the Three Bs, and the finest living interpreter of Brahms.

He continually expanded this reputation with majestic performances of the most difficult Bach compositions and arrangements in the piano literature, often opening his concert seasons with this Bach-Liszt work. From The Brisbane Courier during his whirlwind-success inaugural tour of Australia in 1922: "His opening number was Liszt's transcription of J.S.Bach’s colossal Organ Fantasia and Fugue in G Minor … The composition is one of the very greatest and richest of the master's manifestations of his genius. It is characterised by all the elements of bravura, the weightiest and most surprising progressions of harmony, variety, volume of tone, and contrast of feeling, all infused with the fullest interest of detail. Only a great artist could do justice to its majesty. M. Spivakovsky invested it with the qualities which have already been particularised as indicative of his marvellous power, and by the magnificence of his playing literally brought down the house."

From the Auckland Star during his equally successful inaugural tour of New Zealand the same year: "… a remarkable pianist, and specially successful in Bach, Brahms and Chopin. Everything he does is marked with true earnestness and sincerity, and he never tries to attract those in front by a display of his virtuosity ... Spivakovsky opened with the Bach-Liszt Organ Fantasia and Fugue in G Minor … the initial Grave was given with strength of tone in the majestic chordal parts, whilst the embellishments and figuration of demi-semiquavers were executed with neatness and facility, and the marcatissimo passages received just the requisite weight of tone to exhibit the parts. The Fugue was rendered in a concise and clearly expressed manner, delightfully displaying the intrinsic value of its melodious character and classic design." And a Delhi newspaper during his inaugural tour of India in the 1950s: "The grand introduction of the Fantasia and the deliciously clear rhythm of the Fugue were rendered with superb artistry and musicianship."

His reputation as a master exponent of Beethoven grew rapidly after Bach to Brahms. Chief amongst his admirers in this regard was his friend and colleague Artur Schnabel, who gave him a photographic portrait in 1938 with the inscription "in old admiration and warmest comradeship." Spivakovsky had huge respect for Schnabel as an interpreter of Beethoven and the two often discussed the Beethoven piano sonatas when they lived around the corner from each other in Berlin’s Golden Twenties. During one of these discussions, Spivakovsky showed Schnabel a fingering he had developed for the coda of the Waldstein sonata (which later appeared as a footnote to the Schnabel edition of the Beethoven sonatas, which were first published in 1924 and mentioned “the fingerings and pedal indications are almost without exception by the editor”). To quote Wikipedia: "the coda's glissando octaves, written in dialogue between the hands, compel even advanced performers to play in a simplified version." The generally employed alternative, playing slower staccato octaves, forces exponents to artificially reduce the tempo of the whole movement in order to preserve the contrast between the allegretto rondo and the prestissimo coda. However the fingering developed by Spivakovsky enables every note of the coda to be played prestissimo, as written by Beethoven.

Spivakovsky became recognised as unsurpassable in Beethoven, his playing described by legendary British critic Sir Neville Cardus as "An experience of mind and spirit and a sincere artist’s submergence of self and technical awareness into the world of Beethoven." His postwar interpretations in particular astounded the most discerning critics. John Sinclair, chief critic at The Herald (and one of the chief reasons William Kapell furiously declared at the end of his 1953 tour of Australia "This is goodbye forever – I shall never return"), wrote after an all-Beethoven concert in 1947: "From whatever angle one viewed the performance it was stamped with unmistakeable signs of rarity and greatness … I have never seen an artist sit at the keyboard with less apparent concern for its existence other than as a medium for the realisation of a long-matured imaginative conception. So inflexible is Spivakovsky’s mental control that not a bravura passage in all the four sonatas escaped its relationship to the interpretive whole. Recalling the performance today, I have the choice between futile and inadequate language and silence."

Spivakovsky infuses this famous Ballade with all the fire and poetry which made him "King in the realm of Chopin." From reviews during his wildly successful inaugural tour of Australia in 1922, the Sydney Morning Herald: "Mr Spivakovsky played the Ballade in G Minor with subtle feeling for its underlying melancholy, followed by a powerful grasp of the climax at the close." The Argus: “The G minor Ballade … ranked with the best of the pianist's Chopin interpretations in its fine blend of poetry and elevation." And The Mail: "The breadth of interpretation of the various themes were wrought out with artistic emphasis. The approval of the audience was electrical, and an encore irresistible." From Allgemeine Musikzeitung after a Berlin recital in 1925: "an expansive program placing extraordinary physical and mental demands on the resilience of the pianist, ranging from Bach and Beethoven through Chopin and Liszt to Debussy, Reger and Palmgren … established that this unusually gifted piano virtuoso, whose beginnings already drew all attention to him, is on a continually upwards trajectory with both technical as well as spiritual-musical development. His musical temperament is intuitively instinctive, rather than thoughtfully reflexive ... his interpretation of the Chopin Ballades was particularly successful."

From his equally successful second tour of Australia in 1929, The Sunday Times: "Ballade in G Minor represents one of the most appealing of Chopin's various moods. The pianist exhibited all the poetic charm and dramatic power of the brilliant writing.” And from his third tour of Australia in 1933, The Argus: "He is the dynamic personality, a pianist of brilliant technical attainments, a virile, compelling artist. His personality and playing are entirely masculine. After his performance of Chopin's Ballade in G Minor, nobody would have questioned the stature of this dominating pianist." And The Advertiser: "Jascha Spivakovsky gave us a new interpretation of Chopin's G Minor Ballade, one that mattered. It was maturely conceived – not Spivakovsky at the expense of Chopin. He inspires a great feeling of confidence. Here is a technique to be envied and a discriminating brain to put it to the best use, as the coda showed."

In this exquisite and highly romantic work, Spivakovsky channels the uniquely expressive German Romanticism which won him the reputation "the finest living interpreter of Brahms." In the front row of his admirers in this regard were his friends and colleagues Pierre Monteux and Artur Rubinstein. Maestro Monteux inscribed a photographic portrait which he presented to Spivakovsky: "With my true admiration and great desire to play with him a Brahms concerto," heavily underlining the final two words. An awestruck Rubinstein greeted Spivakovsky after one concert with: "Your BRAHMS, Jascha … your BRAHMS!!!" and later presented him with a photographic portrait, inscribed "Your old admirer." From a review in The Mail after a 1922 performance in Australia: "… another gem was Brahms’ Romanze, given as an encore, and nothing that Spivakovsky does exceeds the wonderful excellence and delicacy of his interpretation of this class of music."

Unlike many of his contemporaries who specialised in a single composer or period, Spivakovsky was a master interpreter of all musical styles. More unique still, he was able to transition from the Romantic to the modern percussive style without losing the expressive qualities of the music. He championed many modern works, including this dramatic war sonata by Dmitry Kabalevsky. From a review in The Auckland Star after a 1957 performance in New Zealand: "Mr Spivakovsky has a warm sincerity which seems to make every work a personal experience for each member of the audience. He has, too, a superlative and powerful technique which displays a very broad range of expression. His inner feeling for the music emerges most noticeably in slow movements where each bar – and every note – is played with illuminating care. His interpretation of more passionate pieces was undeniably exciting and made his treatment of Kabalevsky's Op. 46 Sonata a memorable experience." And The Age after a 1960 performance in Australia: "He proved himself a master pianist of the first order, with an authoritative and effortless command of the keyboard, and an approach to style in the grand manner … the Kabalevsky sonata is an exhilarating piece, full of vitality ... Mr Spivakovsky’s interpretation shows great insight and understanding of the score."